For a lot of exams this makes sense. However, a referee needs to know the laws without being able to look them up or google them.
But the main problem with non-invigilated exams is that you have no idea who is taking them.
I suspect the FA think it doesn't really matter at grassroots levels, and I suppose they might be right. I got a lot out of just being on promotion but that was mostly discussions between candidates on in-service training days and online groups organised by my county.
As a teacher - totally agree here. I think that exams are there for a reason.
However, if there are many, many more questions that require some sort of looking up to find answers, as an exercise to prove understanding of all of the aspects (with an exceptionally high pass mark), this could be quite effective as it is still testing that they know the stuff.
But yes - you can't beat a good old test!!
Or as I do, call it a quiz and just say that there isn't a pass mark, but a fail mark... And they might have to do a re-quiz...